{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TVT_MVvc02AA"
   },
   "source": [
    "# Generalized Convolutions in JAX\n",
    "\n",
    "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/google/jax/blob/main/docs/notebooks/convolutions.ipynb) [![Open in Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/google/jax/blob/main/docs/notebooks/convolutions.ipynb)\n",
    "\n",
    "JAX provides a number of interfaces to compute convolutions across data, including:\n",
    "\n",
    "- {func}`jax.numpy.convolve` (also {func}`jax.numpy.correlate`)\n",
    "- {func}`jax.scipy.signal.convolve` (also {func}`~jax.scipy.signal.correlate`)\n",
    "- {func}`jax.scipy.signal.convolve2d` (also {func}`~jax.scipy.signal.correlate2d`)\n",
    "- {func}`jax.lax.conv_general_dilated`\n",
    "\n",
    "For basic convolution operations, the `jax.numpy` and `jax.scipy` operations are usually sufficient. If you want to do more general batched multi-dimensional convolution, the `jax.lax` function is where you should start."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ewZEn2X12-Ng"
   },
   "source": [
    "## Basic One-dimensional Convolution\n",
    "\n",
    "Basic one-dimensional convolution is implemented by {func}`jax.numpy.convolve`, which provides a JAX interface for {func}`numpy.convolve`. Here is a simple example of 1D smoothing implemented via a convolution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "0qYLpeZO3Z9-",
    "outputId": "4f6717ac-a062-4a85-8330-d57bf80de384"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from jax import random\n",
    "import jax.numpy as jnp\n",
    "import numpy as np\n",
    "\n",
    "key = random.key(1701)\n",
    "\n",
    "x = jnp.linspace(0, 10, 500)\n",
    "y = jnp.sin(x) + 0.2 * random.normal(key, shape=(500,))\n",
    "\n",
    "window = jnp.ones(10) / 10\n",
    "y_smooth = jnp.convolve(y, window, mode='same')\n",
    "\n",
    "plt.plot(x, y, 'lightgray')\n",
    "plt.plot(x, y_smooth, 'black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dYX1tCVB4XOW"
   },
   "source": [
    "The `mode` parameter controls how boundary conditions are treated; here we use `mode='same'` to ensure that the output is the same size as the input.\n",
    "\n",
    "For more information, see the {func}`jax.numpy.convolve` documentation, or the documentation associated with the original {func}`numpy.convolve` function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5ndvLDIH4rv6"
   },
   "source": [
    "## Basic N-dimensional Convolution\n",
    "\n",
    "For *N*-dimensional convolution, {func}`jax.scipy.signal.convolve` provides a similar interface to that of {func}`jax.numpy.convolve`, generalized to *N* dimensions.\n",
    "\n",
    "For example, here is a simple approach to de-noising an image based on convolution with a Gaussian filter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "Jk5qdnbv6QgT",
    "outputId": "292205eb-aa09-446f-eec2-af8c23cfc718"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import misc\n",
    "import jax.scipy as jsp\n",
    "\n",
    "fig, ax = plt.subplots(1, 3, figsize=(12, 5))\n",
    "\n",
    "# Load a sample image; compute mean() to convert from RGB to grayscale.\n",
    "image = jnp.array(misc.face().mean(-1))\n",
    "ax[0].imshow(image, cmap='binary_r')\n",
    "ax[0].set_title('original')\n",
    "\n",
    "# Create a noisy version by adding random Gaussian noise\n",
    "key = random.key(1701)\n",
    "noisy_image = image + 50 * random.normal(key, image.shape)\n",
    "ax[1].imshow(noisy_image, cmap='binary_r')\n",
    "ax[1].set_title('noisy')\n",
    "\n",
    "# Smooth the noisy image with a 2D Gaussian smoothing kernel.\n",
    "x = jnp.linspace(-3, 3, 7)\n",
    "window = jsp.stats.norm.pdf(x) * jsp.stats.norm.pdf(x[:, None])\n",
    "smooth_image = jsp.signal.convolve(noisy_image, window, mode='same')\n",
    "ax[2].imshow(smooth_image, cmap='binary_r')\n",
    "ax[2].set_title('smoothed');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Op-NhXy39z2U"
   },
   "source": [
    "Like in the one-dimensional case, we use `mode='same'` to specify how we would like edges to be handled. For more information on available options in *N*-dimensional convolutions, see the {func}`jax.scipy.signal.convolve` documentation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bxuUjFVG-v1h"
   },
   "source": [
    "## General Convolutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0pcn2LeS-03b"
   },
   "source": [
    "For the more general types of batched convolutions often useful in the context of building deep neural networks, JAX and XLA offer the very general N-dimensional __conv_general_dilated__ function, but it's not very obvious how to use it.  We'll give some examples of the common use-cases.\n",
    "\n",
    "A survey of the family of convolutional operators, [a guide to convolutional arithmetic](https://arxiv.org/abs/1603.07285), is highly recommended reading!\n",
    "\n",
    "Let's define a simple diagonal edge kernel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "Yud1Y3ss-x1K",
    "outputId": "3185fba5-1ad7-462f-96ba-7ed1b0c3d5a2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Edge Conv kernel:\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2D kernel - HWIO layout\n",
    "kernel = jnp.zeros((3, 3, 3, 3), dtype=jnp.float32)\n",
    "kernel += jnp.array([[1, 1, 0],\n",
    "                     [1, 0,-1],\n",
    "                     [0,-1,-1]])[:, :, jnp.newaxis, jnp.newaxis]\n",
    "\n",
    "print(\"Edge Conv kernel:\")\n",
    "plt.imshow(kernel[:, :, 0, 0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dITPaPdh_cMI"
   },
   "source": [
    "And we'll make a simple synthetic image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "cpbGsIGa_Qyx",
    "outputId": "d7c5d21f-c3a0-42e9-c9bc-3da1a508c0e7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Image:\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NHWC layout\n",
    "img = jnp.zeros((1, 200, 198, 3), dtype=jnp.float32)\n",
    "for k in range(3):\n",
    "  x = 30 + 60*k\n",
    "  y = 20 + 60*k\n",
    "  img = img.at[0, x:x+10, y:y+10, k].set(1.0)\n",
    "\n",
    "print(\"Original Image:\")\n",
    "plt.imshow(img[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_m90y74OWorG"
   },
   "source": [
    "### lax.conv and lax.conv_with_general_padding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Pv9_QPDnWssM"
   },
   "source": [
    "These are the simple convenience functions for convolutions\n",
    "\n",
    "️⚠️ The convenience `lax.conv`, `lax.conv_with_general_padding` helper function assume __NCHW__ images and __OIHW__ kernels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "kppxbxpZW0nb",
    "outputId": "9fc5494c-b443-4e74-fe48-fac09e12378c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out shape:  (1, 3, 200, 198)\n",
      "First output channel:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from jax import lax\n",
    "out = lax.conv(jnp.transpose(img,[0,3,1,2]),    # lhs = NCHW image tensor\n",
    "               jnp.transpose(kernel,[3,2,0,1]), # rhs = OIHW conv kernel tensor\n",
    "               (1, 1),  # window strides\n",
    "               'SAME') # padding mode\n",
    "print(\"out shape: \", out.shape)\n",
    "print(\"First output channel:\")\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.imshow(np.array(out)[0,0,:,:]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "id": "aonr1tWvYCW9",
    "outputId": "3d44d494-9620-4736-e331-c9569a4888cd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out shape:  (1, 3, 202, 200)\n",
      "First output channel:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = lax.conv_with_general_padding(\n",
    "  jnp.transpose(img,[0,3,1,2]),    # lhs = NCHW image tensor\n",
    "  jnp.transpose(kernel,[2,3,0,1]), # rhs = IOHW conv kernel tensor\n",
    "  (1, 1),  # window strides\n",
    "  ((2,2),(2,2)), # general padding 2x2\n",
    "  (1,1),  # lhs/image dilation\n",
    "  (1,1))  # rhs/kernel dilation\n",
    "print(\"out shape: \", out.shape)\n",
    "print(\"First output channel:\")\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.imshow(np.array(out)[0,0,:,:]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lyOwGRez_ycJ"
   },
   "source": [
    "### Dimension Numbers define dimensional layout for conv_general_dilated\n",
    "\n",
    "The important argument is the 3-tuple of axis layout arguments:\n",
    "(Input Layout, Kernel Layout, Output Layout)\n",
    " - __N__ - batch dimension\n",
    " - __H__ - spatial height\n",
    " - __W__ - spatial width\n",
    " - __C__ - channel dimension\n",
    " - __I__ - kernel _input_ channel dimension\n",
    " - __O__ - kernel _output_ channel dimension\n",
    "\n",
    "⚠️ To demonstrate the flexibility of dimension numbers we choose a __NHWC__ image and __HWIO__ kernel convention for `lax.conv_general_dilated` below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "id": "oXKebfCb_i2B",
    "outputId": "d5a569b3-febc-4832-f725-1d5e8fd31b9b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ConvDimensionNumbers(lhs_spec=(0, 3, 1, 2), rhs_spec=(3, 2, 0, 1), out_spec=(0, 3, 1, 2))\n"
     ]
    }
   ],
   "source": [
    "dn = lax.conv_dimension_numbers(img.shape,     # only ndim matters, not shape\n",
    "                                kernel.shape,  # only ndim matters, not shape \n",
    "                                ('NHWC', 'HWIO', 'NHWC'))  # the important bit\n",
    "print(dn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "elZys_HzFVG6"
   },
   "source": [
    "#### SAME padding, no stride, no dilation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "rgb2T15aFVG6",
    "outputId": "9b33cdb0-6959-4c88-832a-b92c4e42ae72"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out shape:  (1, 200, 198, 3)\n",
      "First output channel:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = lax.conv_general_dilated(img,    # lhs = image tensor\n",
    "                               kernel, # rhs = conv kernel tensor\n",
    "                               (1,1),  # window strides\n",
    "                               'SAME', # padding mode\n",
    "                               (1,1),  # lhs/image dilation\n",
    "                               (1,1),  # rhs/kernel dilation\n",
    "                               dn)     # dimension_numbers = lhs, rhs, out dimension permutation\n",
    "print(\"out shape: \", out.shape)\n",
    "print(\"First output channel:\")\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.imshow(np.array(out)[0,:,:,0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "E4i3TI5JFVG9"
   },
   "source": [
    "#### VALID padding, no stride, no dilation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "1HQwudKVFVG-",
    "outputId": "be9d6b26-8e3e-44d9-dbd2-df2f6bbf98c2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out shape:  (1, 198, 196, 3) DIFFERENT from above!\n",
      "First output channel:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = lax.conv_general_dilated(img,     # lhs = image tensor\n",
    "                               kernel,  # rhs = conv kernel tensor\n",
    "                               (1,1),   # window strides\n",
    "                               'VALID', # padding mode\n",
    "                               (1,1),   # lhs/image dilation\n",
    "                               (1,1),   # rhs/kernel dilation\n",
    "                               dn)      # dimension_numbers = lhs, rhs, out dimension permutation\n",
    "print(\"out shape: \", out.shape, \"DIFFERENT from above!\")\n",
    "print(\"First output channel:\")\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.imshow(np.array(out)[0,:,:,0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VYKZdqLIFVHB"
   },
   "source": [
    "#### SAME padding, 2,2 stride, no dilation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "id": "mKq2-zmmFVHC",
    "outputId": "14cc0114-e230-4555-a682-23e00b534863"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out shape:  (1, 100, 99, 3)  <-- half the size of above\n",
      "First output channel:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = lax.conv_general_dilated(img,    # lhs = image tensor\n",
    "                               kernel, # rhs = conv kernel tensor\n",
    "                               (2,2),  # window strides\n",
    "                               'SAME', # padding mode\n",
    "                               (1,1),  # lhs/image dilation\n",
    "                               (1,1),  # rhs/kernel dilation\n",
    "                               dn)     # dimension_numbers = lhs, rhs, out dimension permutation\n",
    "print(\"out shape: \", out.shape, \" <-- half the size of above\")\n",
    "plt.figure(figsize=(10,10))\n",
    "print(\"First output channel:\")\n",
    "plt.imshow(np.array(out)[0,:,:,0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gPxttaiaFVHE"
   },
   "source": [
    "#### VALID padding, no stride, rhs kernel dilation ~ Atrous convolution (excessive to illustrate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "id": "_pGr0x6qFVHF",
    "outputId": "9edbccb6-d976-4b55-e0b7-e6f3b743e476"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out shape:  (1, 176, 174, 3)\n",
      "First output channel:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = lax.conv_general_dilated(img,     # lhs = image tensor\n",
    "                               kernel,  # rhs = conv kernel tensor\n",
    "                               (1,1),   # window strides\n",
    "                               'VALID', # padding mode\n",
    "                               (1,1),   # lhs/image dilation\n",
    "                               (12,12), # rhs/kernel dilation\n",
    "                               dn)      # dimension_numbers = lhs, rhs, out dimension permutation\n",
    "print(\"out shape: \", out.shape)\n",
    "plt.figure(figsize=(10,10))\n",
    "print(\"First output channel:\")\n",
    "plt.imshow(np.array(out)[0,:,:,0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "v-RhEeUfFVHI"
   },
   "source": [
    "#### VALID padding, no stride, lhs=input dilation  ~ Transposed Convolution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "id": "B9Ail8ppFVHJ",
    "outputId": "7aa19474-566f-4419-bfae-8286dd026c1c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out shape:  (1, 397, 393, 3) <-- larger than original!\n",
      "First output channel:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = lax.conv_general_dilated(img,               # lhs = image tensor\n",
    "                               kernel,            # rhs = conv kernel tensor\n",
    "                               (1,1),             # window strides\n",
    "                               ((0, 0), (0, 0)),  # padding mode\n",
    "                               (2,2),             # lhs/image dilation\n",
    "                               (1,1),             # rhs/kernel dilation\n",
    "                               dn)                # dimension_numbers = lhs, rhs, out dimension permutation\n",
    "print(\"out shape: \", out.shape, \"<-- larger than original!\")\n",
    "plt.figure(figsize=(10,10))\n",
    "print(\"First output channel:\")\n",
    "plt.imshow(np.array(out)[0,:,:,0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "A-9OagtrVDyV"
   },
   "source": [
    "We can use the last to, for instance, implement _transposed convolutions_:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "id": "5EYIj77-NdHE",
    "outputId": "f45b16f7-cc6e-4593-8aca-36b4152c3dfa"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out shape:  (1, 400, 396, 3) <-- transposed_conv\n",
      "First output channel:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The following is equivalent to tensorflow:\n",
    "# N,H,W,C = img.shape\n",
    "# out = tf.nn.conv2d_transpose(img, kernel, (N,2*H,2*W,C), (1,2,2,1))\n",
    "\n",
    "# transposed conv = 180deg kernel rotation plus LHS dilation\n",
    "# rotate kernel 180deg:\n",
    "kernel_rot = jnp.rot90(jnp.rot90(kernel, axes=(0,1)), axes=(0,1))\n",
    "# need a custom output padding:\n",
    "padding = ((2, 1), (2, 1))\n",
    "out = lax.conv_general_dilated(img,     # lhs = image tensor\n",
    "                               kernel_rot,  # rhs = conv kernel tensor\n",
    "                               (1,1),   # window strides\n",
    "                               padding, # padding mode\n",
    "                               (2,2),   # lhs/image dilation\n",
    "                               (1,1),   # rhs/kernel dilation\n",
    "                               dn)      # dimension_numbers = lhs, rhs, out dimension permutation\n",
    "print(\"out shape: \", out.shape, \"<-- transposed_conv\")\n",
    "plt.figure(figsize=(10,10))\n",
    "print(\"First output channel:\")\n",
    "plt.imshow(np.array(out)[0,:,:,0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "v8HsE-NCmUxx"
   },
   "source": [
    "### 1D Convolutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WeP0rw0tm7HK"
   },
   "source": [
    "You aren't limited to 2D convolutions, a simple 1D demo is below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "id": "jJ-jcAn3cig-",
    "outputId": "67c46ace-6adc-4c47-c1c7-1f185be5fd4b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in shapes: (1, 200, 2) (3, 2, 2)\n",
      "ConvDimensionNumbers(lhs_spec=(0, 2, 1), rhs_spec=(2, 1, 0), out_spec=(0, 2, 1))\n",
      "out shape:  (1, 200, 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1D kernel - WIO layout\n",
    "kernel = jnp.array([[[1, 0, -1], [-1,  0,  1]], \n",
    "                    [[1, 1,  1], [-1, -1, -1]]], \n",
    "                    dtype=jnp.float32).transpose([2,1,0])\n",
    "# 1D data - NWC layout\n",
    "data = np.zeros((1, 200, 2), dtype=jnp.float32)\n",
    "for i in range(2):\n",
    "  for k in range(2):\n",
    "      x = 35*i + 30 + 60*k\n",
    "      data[0, x:x+30, k] = 1.0\n",
    "\n",
    "print(\"in shapes:\", data.shape, kernel.shape)\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(data[0]);\n",
    "dn = lax.conv_dimension_numbers(data.shape, kernel.shape,\n",
    "                                ('NWC', 'WIO', 'NWC'))\n",
    "print(dn)\n",
    "\n",
    "out = lax.conv_general_dilated(data,   # lhs = image tensor\n",
    "                               kernel, # rhs = conv kernel tensor\n",
    "                               (1,),   # window strides\n",
    "                               'SAME', # padding mode\n",
    "                               (1,),   # lhs/image dilation\n",
    "                               (1,),   # rhs/kernel dilation\n",
    "                               dn)     # dimension_numbers = lhs, rhs, out dimension permutation\n",
    "print(\"out shape: \", out.shape)\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(out[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7XOgXqCTmaPa"
   },
   "source": [
    "### 3D Convolutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "id": "QNvSiq5-mcLd",
    "outputId": "c99ec88c-6d5c-4acd-c8d3-331f026f5631"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in shapes: (1, 30, 30, 30, 1) (3, 3, 3, 1, 1)\n",
      "ConvDimensionNumbers(lhs_spec=(0, 4, 1, 2, 3), rhs_spec=(4, 3, 0, 1, 2), out_spec=(0, 4, 1, 2, 3))\n",
      "out shape:  (1, 30, 30, 30, 1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "\n",
    "# Random 3D kernel - HWDIO layout\n",
    "kernel = jnp.array([\n",
    "  [[0, 0,  0], [0,  1,  0], [0,  0,   0]],\n",
    "  [[0, -1, 0], [-1, 0, -1], [0,  -1,  0]], \n",
    "  [[0, 0,  0], [0,  1,  0], [0,  0,   0]]], \n",
    "  dtype=jnp.float32)[:, :, :, jnp.newaxis, jnp.newaxis]\n",
    "\n",
    "# 3D data - NHWDC layout\n",
    "data = jnp.zeros((1, 30, 30, 30, 1), dtype=jnp.float32)\n",
    "x, y, z = np.mgrid[0:1:30j, 0:1:30j, 0:1:30j]\n",
    "data += (jnp.sin(2*x*jnp.pi)*jnp.cos(2*y*jnp.pi)*jnp.cos(2*z*jnp.pi))[None,:,:,:,None]\n",
    "\n",
    "print(\"in shapes:\", data.shape, kernel.shape)\n",
    "dn = lax.conv_dimension_numbers(data.shape, kernel.shape,\n",
    "                                ('NHWDC', 'HWDIO', 'NHWDC'))\n",
    "print(dn)\n",
    "\n",
    "out = lax.conv_general_dilated(data,    # lhs = image tensor\n",
    "                               kernel,  # rhs = conv kernel tensor\n",
    "                               (1,1,1), # window strides\n",
    "                               'SAME',  # padding mode\n",
    "                               (1,1,1), # lhs/image dilation\n",
    "                               (1,1,1), # rhs/kernel dilation\n",
    "                               dn)      # dimension_numbers\n",
    "print(\"out shape: \", out.shape)\n",
    "\n",
    "# Make some simple 3d density plots:\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "def make_alpha(cmap):\n",
    "  my_cmap = cmap(jnp.arange(cmap.N))\n",
    "  my_cmap[:,-1] = jnp.linspace(0, 1, cmap.N)**3\n",
    "  return mpl.colors.ListedColormap(my_cmap)\n",
    "my_cmap = make_alpha(plt.cm.viridis)\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.scatter(x.ravel(), y.ravel(), z.ravel(), c=data.ravel(), cmap=my_cmap)\n",
    "ax.axis('off')\n",
    "ax.set_title('input')\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.scatter(x.ravel(), y.ravel(), z.ravel(), c=out.ravel(), cmap=my_cmap)\n",
    "ax.axis('off')\n",
    "ax.set_title('3D conv output');"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "convolutions.ipynb",
   "provenance": []
  },
  "jupytext": {
   "formats": "ipynb,md:myst"
  },
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